V. V. Aseev, “Generalized angles in Ptolemaic Möbius structures”, Sibirsk. Mat. Zh., 59:2 (2018), 241–256; Siberian Math. J., 59:2 (2018), 189

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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 2, Pages 241–256
DOI: https://doi.org/10.17377/smzh.2018.59.201 (Mi smj2968)

This article is cited in 16 scientific papers (total in 16 papers)

Generalized angles in Ptolemaic Möbius structures

V. V. Aseev

Sobolev Institute of Mathematics, Novosibirsk, Russia

Full-text PDF (357 kB) Citations (16)

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DOI: https://doi.org/10.17377/smzh.2018.59.201

Abstract: We show that each Ptolemaic semimetric is Möbius-equivalent to a bounded metric. Introducing generalized angles in Ptolemaic Möbius structures, we study the class of multivalued mappings

$F\colon X\to2^Y$ with a lower bound on the distortion of generalized angles. We prove that the inverse mapping to the coordinate function of a quasimeromorphic automorphism of

$\overline{\mathbb R}^n$ lies in this class.

Keywords: Möbius structure, Ptolemy's inequality, Ptolemaic semimetric, angular metric, Möbius-invariant metric, quasimöbius mapping, generalized angle, quasimeromorphic mapping.

Funding agency	Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations	1.1.2, проект 0314-2016-0007
The author was supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. 1.1.2, Project 0314-2016-0007).

Received: 14.07.2017

English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 2, Pages 189–201
DOI: https://doi.org/10.1134/S0037446618020015

Bibliographic databases:

Document Type: Article

UDC: 517.54

MSC: 35R30

Language: Russian

Citation: V. V. Aseev, “Generalized angles in Ptolemaic Möbius structures”, Sibirsk. Mat. Zh., 59:2 (2018), 241–256; Siberian Math. J., 59:2 (2018), 189–201

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Linking options:

https://www.mathnet.ru/eng/smj2968

https://www.mathnet.ru/eng/smj/v59/i2/p241

Cycle of papers

Generalized angles in Ptolemaic Möbius structures
V. V. Aseev
Sibirsk. Mat. Zh., 2018, 59:2, 241–256
Generalized angles in Ptolemaic Möbius structures. II
V. V. Aseev
Sibirsk. Mat. Zh., 2018, 59:5, 976–987

This publication is cited in the following 16 articles:

V. V. Aseev, “The Ptolemaic Characteristic of Tetrads and Quasiregular Mappings”, Sib Math J, 65:5 (2024), 995
V. V. Aseev, “Ptolemeeva kharakteristika tetrad i kvaziregulyarnye otobrazheniya”, Sib. matem. zhurn., 65:5 (2024), 785–794
V. V. Aseev, “Mnogoznachnye kvazimëbiusovy otobrazheniya na rimanovoi sfere”, Sib. matem. zhurn., 64:3 (2023), 450–464
N. V. Abrosimov, V. V. Aseev, “Multivalued quasimöbius property and bounded turning”, Sib. elektron. matem. izv., 20:2 (2023), 1185–1199
V. V. Aseev, “Graficheskie predely kvazimeromorfnykh otobrazhenii i iskazhenie kharakteristiki tetrad”, Sib. matem. zhurn., 64:6 (2023), 1138–1150
Zhiqiang Yang, Qingshan Zhou, “Topological Angles and Freely Quasiconformal Mappings in Real Banach Spaces”, Comput. Methods Funct. Theory, 23:2 (2023), 347
V. V. Aseev, “The Multi-Valued Quasimöbius Mappings on the Riemann Sphere”, Sib Math J, 64:3 (2023), 514
V. V. Aseev, “Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads”, Sib Math J, 64:6 (2023), 1279
V. V. Aseev, “Bounded turning in Möbius structures”, Siberian Math. J., 63:5 (2022), 819–833
V. V. Aseev, “Multivalued quasimöbius mappings from circle to circle”, Siberian Math. J., 62:1 (2021), 14–22
V. V. Aseev, “Some remarks on Möbius structures”, Sib. elektron. matem. izv., 18:1 (2021), 160–167
V. V. Aseev, “Adherence of the images of points under multivalued quasimöbius mappings”, Siberian Math. J., 61:3 (2020), 391–402
V. V. Aseev, “Rectangle as a generalized angle”, Sib. elektron. matem. izv., 16 (2019), 2013–2018
V. V. Aseev, “Multivalued mappings with the quasimöbius property”, Siberian Math. J., 60:5 (2019), 741–756
V. V. Aseev, “On coordinate vector-functions of quasiregular mappings”, Sib. elektron. matem. izv., 15 (2018), 768–772
V. V. Aseev, “Generalized angles in Ptolemaic Möbius structures. II”, Siberian Math. J., 59:5 (2018), 768–777

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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